1)log4 80/ (2 + log4 5) 2) log 2(корень из 15)

1)log₄ 80/ (2 + log₄ 5) = log₄ 80/(2log₄ 4 + log₄ 5) = log₄ 80/(log₄ 4² + log₄ 5) = log₄ 80/ log₄ (16 * 5) = log₄ 80/ log₄ 80 = 1;

2) log_2(sqrt15) 3375 = log_2(sqrt15) 15³ = 3 log_2(sqrt15) 15 = 3 * log₁₅ 15/log₁₅ 2sqrt15 = 3/(log₁₅ sqrt15 + log₁₅ 2) = 3/(1/2 + log₁₅ 2);

3) log 16 * log₂ 16 = log₁₆ log₂ 2^4 = log₁₆ 4 = log_4^2 4 = 1/2;

4) log_2/5 sqrt2,5 = log_2/5 sqrt5/2 = log_2/5 5/2^1/2 = 1/2log_2/5 5/2 = 1/2 * (-1) = -1/2;

5) log₉ 25(sqrt12)/ log₉ 12 = log₉ 12^1/25/log₉ 12 = 1/25.